The = 1 superconformal index for class fixed points View Full Text


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Article Info

DATE

2014-04-07

AUTHORS

Christopher Beem, Abhijit Gadde

ABSTRACT

We investigate the superconformal index of four-dimensional superconformal field theories that arise on coincident M5 branes wrapping a holomorphic curve in a local Calabi-Yau three-fold. The structure of the index is very similar to that which appears in the special case preserving \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 2 supersymmetry. We first compute the index for the fixed points that admit a known four-dimensional ultraviolet description and prove infrared equivalence at the level of the index for all such constructions. These results suggest a formulation of the index as a two-dimensional topological quantum field theory that generalizes the one that computes the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 2 index. The TQFT structure leads to an expression for the index of a much larger family of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 1 class S fixed points in terms of the index of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 2 theories. Calculations of simple quantities with the index suggests a connection between these families of fixed points and the mathematics of SU(2) Yang-Mills theory on the wrapped curve. More... »

PAGES

36

References to SciGraph publications

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  • 2010-08-24. The superconformal index of the E6 SCFT in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-06-01. Four-dimensional SCFTs from M5-branes in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-02-05. Holographic Uniformization in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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  • 2011-03-09. On the superconformal index of IR fixed points. A holographic check in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2013-06-13. New =1 dualities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-03-08. S-duality and 2d topological QFT in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2010-07-01. Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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